A wavelet method, commercialized as a result of recent developments of computer technology, is used to search for signs in time-series data in a state-monitoring system. The wavelet method is inferior to Fourier transform in terms of accuracy of spectrum analysis but it is capable of dynamic analysis. The wavelet method more accurately captures spectral changes in both time-series data and images. Currently, the wavelet method is extensively used to detect signs in time-series data and recognize images in image data.
FIGS. 37 and 38 show the structure of a waveform detection system based on the existing wavelet method (hereafter called the wavelet system). The wavelet system comprises, as shown in the figures, a sensor 3, signal input 1, computer 9, determinator 20, and output 25. Input signals are processed at the computer 9 to detect waveforms.
As shown in FIG. 37, the signal input comprises a converter 2 that collects data from the sensor 3, A/D converter 4, memory 5, and data fetcher 7. Measurement values from the sensor 3 are converted into digital data by the A/D converter 4. Input signals are stored in files in the memory 5. Data are supplied for further processing at the computer. The necessary measurement input signal data 8 are created at the computer 9.
The computer 9 comprises a signal processor 11, digital filter calculator 13 comprising multiple digital filters Df1-Dfn, a parameter setter 15, and a synthesizer 17 that integrates the outputs from the digital filters Df1-Dfn. The signal processor 11 at the computer 9 is not essential but can be included as if required. Individually, the signal processor processes noise in the input signals, normalizes data, and distributes multiple data.
The structure of the digital filters Df1-Dfn in the computer is described as shown in FIGS. 39 and 40. In FIG. 37, each digital filter Df comprises a delay memory 16 that stores and delays input signals, and a multiplication coefficient pattern memory 14 that stores multiplication coefficients. In FIG. 38, the parameter setter 15 has a filter parameter setter 29 and a multiplication coefficient pattern setter 30. The computer 9 has a delay memory 16 on the digital filters Df1-Dfn.
As shown in FIG. 40, the digital filter Df outputs the sums of products of input signals and preset multiplication coefficient patterns. The output is large when a waveform close to the shape of the multiplication coefficient pattern is present in the input signals. As shown in FIG. 39, the data in the memory is carried forward as new data enters the memory, so that the filter Df outputs the characteristics at that time together with the time increment. The array of the outputs is thus a distribution of component intensities at a given time, showing the signal characteristics. If the combination of characteristics correlates with the pattern of certain time-series data or the shape of a symbol code, it is possible to detect signs showing variations in the state of time-series data, identify and fetch symbols or codes of an image, or predict changes in input waveforms by highlighting a portion of the fluctuation components of an input signal.
FIG. 46 shows how input signals are processed on a conventional digital filter computer. Three kinds of digital filters perform multiplication individually for the same input signal and the products are summed and synthesized at the synthesizer to generate the output. In this example, different filter shapes are used and three types of outputs each extracting the characteristics of the waveforms are summed to detect the waveform.
The determinator 20 in FIG. 37 compares the synthesized output (digital filter output) from the computer 9 with the threshold value to determine the size difference and derive a result of determination (Ds−j). The output could be a monitor 26 that shows the result of the determination, or an alarm device 28 such as a lamp connected via a contact output 27.
In the wavelet system shown in FIG. 41, multiple digital filter multiplication coefficient patterns are matched to a function pattern called an elemental pattern. Multiple short-period similar patterns are generated from the elemental pattern to determine the intensity of the frequency components. The shape of the elemental pattern determines which components are extracted from the incoming signal. These similar patterns are used to generate filters of a different frequency band to match the length of the multiplication coefficient pattern. The multiplication coefficient pattern also determines the type of signal processing used, such as integration and differentiation, so that once the elemental pattern is determined multiple digital filters with a similar multiplication coefficient pattern perform the same signal processing where only the frequency band is different. In the wavelet system, the scale (length along the time axis) of the basic multiplication coefficient pattern for identifying correlations with input signals is equal to the length of several wavelengths of the respective frequencies. Thus, compared with Fourier transform, the wavelet system can analyze power spectra of a relatively short time interval.
In FIG. 42, a multiplication coefficient pattern typically used in a conventional wavelet system is used to derive the digital filter outputs from an input signal. A wavelet generally has a scale several times longer than the wavelength of the lowest frequency to be characterized. The reference time axis is positioned at the, center of the multiplication coefficient pattern column. The pattern extends on both sides of the axis in the same phase. Some effective output is derived when the input signal arrives at the center of the delay memory with a sequential delay, and an inner product is calculated with the coefficient located at the center of the pattern column. This means that a detection delay proportional to the wavelength always exists when identifying input signal data using this type of multiplication coefficient pattern.
The wavelet is suitable for analyzing cyclic signals that last for a certain time period. It has been used for analyzing voice and vibrations of a certain length, and also for textures (image quality, elemental patterns, etc.) that extend over a certain distance. The signs embedded in time-series data do not have vibration components in many cases. The difference in texture between the entire time-series data and the area containing signs is small as the scale of the multiplication coefficient pattern becomes larger. It is thus difficult to detect a transient decrease in this case. The size of the scale is a major problem in analyzing non-cyclic signals with small repetitive vibrations or small-area images. It is difficult for the wavelets to characterize one-time pulses such as those in the input signals shown in FIGS. 31A, 31B, 31C and 31D. This is because the wavelet focuses on the damping curves and undulation of specified sounds, and as such, it does not effectively identify signals by sound reverberation. When the rise and fall of an input signal have a different waveform such as shown in FIG. 42, identifying only the rising waveform is difficult, with the result that the normal waveform WA and abnormal waveform WB are not differentiated, and the system reacts strongly to the normal waveform WC.
Apart from the above, many studies are being undertaken to realize human-friendly control by performing 1/f fluctuation conversion for input waveforms. FIG. 43 shows a typical conventional 1/f fluctuation waveform generator. Conventional low-pass (LPF) and high-pass filters (HPF) are combined to approximately generate the 1/f fluctuation waveforms. Random waveforms are input and the high-pass filter coefficients are adjusted to derive the 1/f fluctuation waveforms. This means that the characteristic of the conventional low-pass filter is damped by a tilt of −2 or more. The tilt of the target 1/f fluctuation is −1. The high-pass filters with a tilt of 2 or more, which are multiplied by coefficient k, are combined in parallel to make a filter set. Adjusting coefficient k derives a tilt of approximately −1. Filter sets of a different band are connected in series to expand the filter characteristics to a wider frequency region.
The problem with this system is that precision operational amplifiers must be used to construct the target filters with electric elements, and the production involves very large-expenses. To construct the original, the filters of the above hardware are used as the above digital filters, and then filter sets are constructed. This can be achieved relatively easily. For example, the conventional multiplication coefficient pattern-(A) shown in FIG. 29 may be used as the multiplication coefficient pattern of the low-pass filter LPF. High-pass filters HPF can also be configured in like manner. However, low-pass filters (LPFs) and high-pass filters (HPFs) have a different phase gap (difference of time of change between input and output) so that it is difficult to synthesize multiplication coefficient patterns of both filters to generate a new one. A more complex means is required to generate a multiplication coefficient pattern for high-pass filters (HPFs) by converting the value of coefficient k and then synthesizing the patterns of both filters.
The other conventional technique uses ½-time integration. The input is a random progression derived from random functions, and the power spectrum of the output is approximated to 1/f fluctuation. The details have been described in a book (Kazuo Tanaka; Intelligent Control System [Intelligent Control by Fuzzy Neuro, 6A Chaos], Kyoritsu Shuppan Co.). Of the above low-pass filters (LPFs), the digital filter Df with a primary delay with a number of integration equivalent to 1 will generate outputs of the power spectrum with a −2 tilt. To perform a −1 tilt power spectrum conversion, the number of integration is reduced to less than 1 to smooth the random progression. FIGS. 44A, 44B, and 44C show a multiplication coefficient pattern of ½-time integration with 8-tap digital filters Dfs (FIG. 44A), and the resultant conversion outputs (FIGS. 44D and 44C). FIGS. 45A, 45B and 45C show a multiplication coefficient pattern of ⅓-time integration with 8-tap digital filters Dfs (FIG. 45A), and the resultant conversion outputs (FIGS. 45B and 45C). The number of integrations is less than 1 in both cases. To derive a smooth 1/f fluctuation with a −1 tilt, the number of taps must be increased. The power spectrum curve will not be smooth if the number of digital filter taps is small.
In consideration of the above condition, the present invention solves the problems of conventional wavelet systems by:
a. Contrary to the underlying concept of conventional wavelet systems, it ignores frequency separation characteristics and instead maximizes the phase characteristics (ability to identify undulation and other anomalies), and
b. Makes final determination by matching the timing of phase delay (gap of detection time) of multiple filters.
Another objective of the present invention is to solve the above problems of conventional 1/f fluctuation conversion by setting and shaping the digital filter multiplication coefficient patterns using mathematical formulae and software.
The present invention focuses attention on the fact that the digital filters (Dfs) emit outputs by predicting the transition of input waveforms when signals are input and a portion of the fluctuation-components of, the input signal-is-highlighted. The present invention therefore uses digital filters (Dfs) to output 1/f fluctuation waveforms and other specific waveforms using non-integer n-time integration.
The present invention discerns sound and noise and other one-time undulation in time-series data and also identifies the characteristic of individual single pulses (pulsation). As a result, it can be used for predictive diagnosis and determination of acceptance or rejection of merchandise. It is also possible for the system of the present invention to input random waveforms and output specific waveforms with a frequency component distribution such as 1/f fluctuation waveforms. A similar technique is known at this time, in which undulation and pulse waveforms are approximated with a sequential line and the sequential line coordinates are input to discern the difference of patterns in a neural network. This technique involves complex procedures and huge computation overhead so that the system cost is quite high. Furthermore, slow pulses are processed but real-time processing is impossible. The present invention characterizes a wide range of waveforms from pulse sounds containing sharp and high-frequency components to very long cyclic time-series data with little change recurring slowly over a long time period. Furthermore, the processing procedure is not complex. The present invention can also easily output specific waveforms such as 1/f fluctuation waveforms by-effectively using digital filters embedded in the above waveform converter.